In a square-root spiral, which two lengths form the perpendicular sides needed to construct √3?

Correct answer: √2 and 1

Answer: option A, √2 and 1. In a standard square-root spiral, the previous hypotenuse becomes one side of a right triangle, and a new perpendicular segment of length 1 unit is added. To obtain √3, use the preceding hypotenuse √2 together with the unit segment 1. By the Pythagorean theorem, the new hypotenuse h satisfies h² = (√2)² + 1² = 2 + 1 = 3, so h = √3 because lengths are positive. Option B would give √(3+1) = √4, the next stage. Option C gives √8, and option D gives √10. Thus only A produces √3. Memory cue: each step adds one unit square to the square of the previous hypotenuse.